The classical control scheme for a typical switch-mode rectifier as shown in FIG. 1 employs two cascaded feedback control loops; the inner current loop for input current shaping and total harmonic distortion (THD) minimization and the outer voltage loop for output voltage regulation. For minimizing THD average current control is preferred. The inductor current which is used as the feedback signal for average current control is normally sensed using either a resistor in series with the inductor or a magnetic current sensing device such as Hall Effect based current sensor or regular current transformer. Resistor sensing is usually very straightforward, particularly in low power circuits, where the power dissipation in the sense resistor is negligible. However, in many applications, using a current sense resistor in the direct path of the current to be measured is not practical as not only a small value of sense resistor is difficult to implement, but also the power loss in the sense resistor is too high, particularly in large power converters. Also this sense resistor needs connection to the high voltage section of the circuit and hence isolation of the low voltage control circuit can become an issue. Hall Effect current sensors are reliable but suffer from dc offset, higher cost, temperature issues and the need to have a separate power supply. A single ferrite core current transformer (CT) cannot be directly used to sense the inductor current as it has a dc offset. To circumvent this problem two CTs can be used, one for sensing the switch current and one for sensing the diode current. By summing these two currents the true inductor current can be reconstructed [1]. Other options include copper trace resistance sensing with temperature compensation electronics, Rogowski coils, magneto resistance sensors and fiber-optic current sensors. Their applications are limited by isolation issues, high cost, size, incapability of measuring direct currents, low accuracy, or unsuitability for small currents [2,3].
From the above discussion it is clear that there is a need for an accurate, sensorless current measurement or estimation scheme. The vast body of literature related to research on sensorless current estimation techniques also confirms this viewpoint. They are briefly reviewed in the next few paragraphs.
In [4-6], the reference current is generated from input and output voltage without current sensing. The turn-off instant of the switch is calculated based on the maximum value of the reference current in a switching instant. The peak of the ramp carrier signal is proportional to the output dc voltage. The control law makes the peak current in each switching period follow vd. The drive signal delay, sample and hold delays and measured voltage offset error can also be compensated. However compensation technique is utility voltage and load dependent and research is still required to make it tunable for any operating point. The scheme has been implemented using a field programmable gate array (FPGA).
Since under continuous conduction mode (CCM) the input-output relationship of a boost SMR is given by (1), it logically follows that varying a duty cycle, d, which is modulated because of the sinusoidal nature of the voltage waveform vd, would essentially result in a sinusoidal input current; with the output voltage Vo maintained constant by a closed loop controller. Thus researchers followed this lead and came up with many improved versions of this basic scheme [7-11] that add a term which is proportional to the derivative of vd. This is because the derivative of the inductor current iL should be ideally proportional to the instantaneous values of vd as shown by (2). Following FIG. 1, the voltage across the boost inductor L, neglecting the series resistance RL can be written as (3). vQ, the voltage across the switch Q can also be written in terms of the output voltage Vo as (4). Substituting iL and vQ from (2) and (4) respectively in (3) one can obtain an improved version of (1) as shown in (5).
                    ⅆ                  =                      1            -                                          ν                d                                            V                o                                                                        (        1        )                                          i          L                =                              κ            1                    ·                      ν            d                                              (        2        )                                          L          ⁢                                    ⅆ                              i                L                                                    ⅆ              t                                      =                              ν            d                    -                      ν            Q                                              (        3        )                                          ν          Q                =                              (                          1              -              ⅆ                        )                    ⁢                      V            o                                              (        4        )                                ⅆ                  =                      1            -                                          ν                d                                            V                o                                      +                                                                                κ                    2                                    ⁢                  L                                                  V                  o                                            ⁢                                                ⅆ                                      ν                    d                                                                    ⅆ                  t                                                                                        (        5        )            
A further improved version of (5) includes the inductor equivalent series resistance, the voltage drop across the rectifier diodes, and also the drops across the switch and the diode in the boost converter [12]. References [13] and [14] sense only the input voltage to implement (5). Discrete time domain versions of (5) suitable for microcontroller implementation with or without compensating for circuit non-idealities using stored or computed duty cycle patterns have also been examined in [15-19].
A different approach is followed in [20-24] to achieve a current sensorless boost-type SMR. The voltage loop output in the form of a phase angle α, is used to control the output voltage along with the shape of the input current, as given by (6). Compensation for circuit non-idealities such as inductor resistance and device drops are also possible. While most of them are single loop, a two loop implementation, with one loop for phase angle and one for mean output voltage control through real power control; using Kalman filters have been implemented [23].
                              d          =                      1            -                                                                                v                    ^                                    d                                                  v                  0                                            ⁢                                                                sin                  ⁡                                      (                                          θ                      -                      α                                        )                                                                                                      ;                              v            d                    =                                                    v                ^                            d                        ⁢                                                        sin                ⁡                                  (                  θ                  )                                                                                                      (        6        )            
TABLE IPrior-art in the area of current sensorless control of single phase boost-type SMR.[7][10][13][15][21][4-6][8][9][11][12][14][16][17][18][19][20][22][23][24][25]Takes circuitNoNoNoNoYesNoNoYesNoNoNoYesNoYesNonon-idealities into accountProven to beYes1NoYes2NoNoNoNoNoNoNoNo Yes3No Yes4Noinsensitive toparametervariation1Not verified with experimental results.2Analyzed input admittance for inductance variations.3Experimental results have been obtained with non-nominal inductance and capacitance.4Detailed experimental results have been provided on parameter variation.In [25], the current is indirectly measured by connecting a capacitor in series with a resistor across the boost inductor. If vCs(s) and iL(s) are respectively the capacitor voltage and inductor current in frequency domain, it can be shown that
                                                        v                              C                s                                      ⁡                          (              s              )                                                          i              L                        ⁡                          (              s              )                                      =                                                            R                L                            +              sL                                      1              +                                                sR                                      C                    s                                                  ⁢                                  C                  s                                                              =                                                    R                L                            ⁢                                                1                  +                                      s                    ⁢                                          L                                              R                        L                                                                                                              1                  +                                                            sR                                              C                        s                                                              ⁢                    C                                                                        =                                          R                L                            ⁢                                                1                  +                                      s                    ⁢                                                                                  ⁢                                          τ                      L                                                                                        1                  +                                      s                    ⁢                                                                                  ⁢                                          τ                      C                                                                                                                              (        7        )            where RL, RCs are respectively the equivalent series resistance of the boost inductor L and the external resistor connected in series with the current sense capacitor Cs. If τC=RCsCs is chosen so that it matches
            τ      L        =          L              R        L              ,the relation
      v          C      s            i    L  becomes frequency independent, signifying that the sensing preserves the shape of the inductor current. Under this condition, vCs is proportional to the inductor current and therefore can be used in the current control loop. Obviously, the technique is load dependent as both the inductor resistance and the inductor value are influenced by the inductor current. Reference [26] presents a similar technique applied to a dc-dc buck converter using a self-tuning digital filter whose parameters are tuned using a test current sink, consisting of a known resistor in series with a small switch, in parallel with the load. Table I summarizes the prior art in the area of current sensorless control of single phase boost-type SMR.